To determine the dimensions of the product $LC$, we can use the formula for the resonant frequency of an LC circuit or multiply individual dimensions.

1. Using Resonant Frequency Formula: The resonant frequency ($\omega$) is given by the relation $\omega = \frac{1}{\sqrt{LC}}$ . The dimension of angular frequency is $[T^{-1}]$ . Therefore, $[T^{-1}] = [LC]^{-1/2}$.

• Squaring both sides and inverting: $[LC] = [T^2] = [M^0 L^0 T^2]$.

2. Using Individual Dimensions:

• Inductance ($L$): $[ML^2T^{-2}A^{-2}]$ .
• Capacitance ($C$): $[M^{-1}L^{-2}T^4A^2]$ .
• Product $LC$: $[ML^2T^{-2}A^{-2}] \times [M^{-1}L^{-2}T^4A^2]$ $= [M^{1-1} L^{2-2} T^{-2+4} A^{-2+2}]$ $= [M^0 L^0 T^2]$